Estimation and tracking of rapidly time-varying broadband acoustic communication channels

Abstract

This thesis develops methods for estimating wideband shallow-water acoustic communication channels. The very shallow water wideband channel has three distinct features: large dimension caused by extensive delay spread; limited number of degrees of freedom (DOF) due to resolvable paths and inter-path correlations; and rapid fluctuations induced by scattering from the moving sea surface. Traditional LS estimation techniques often fail to reconcile the rapid fluctuations with the large dimensionality. Subspace based approaches with DOF reduction are confronted with unstable subspace structure subject to significant changes over a short period of time.Based on state-space channel modeling, the first part of this thesis develops algorithms that jointly estimate the channel as well as its dynamics. Algorithms based on the Extended Kalman Filter (EKF) and the Expectation Maximization (EM) approach respectively are developed. Analysis shows conceptual parallels, including an identical second-order innovation form shared by the EKF modification and the suboptimal EM, and the shared issue of parameter identifiability due to channel structure, reflected as parameter unobservability in EKF and insufficient excitation in EM. Modifications of both algorithms, including a two-model based EKF and a subspace EM algorithm which selectively track dominant taps and reduce prediction error, are proposed to overcome the identifiability issue. The second part of the thesis develops algorithms that explicitly find the sparse estimate of the delay-Doppler spread function.The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.

A Review of Sparse Recovery Algorithms

“…Comparing with the LS cost function, it is possible to see that ( 14) basically includes a l 1 norm penalty term. Hence, under certain conditions, the solution would achieve the minimal LS error [115]. Since h 1 is not differentiable for any zero position of h, it is not possible to obtain an analytical solution for the global minimum of (14).…”

“…This work presents some sparse recovery algorithms. However, if the reader wants to know other algorithms, in addition to the vast list presented above, some of them can be found in: Back-tracking based Adaptive Orthogonal Matching Pursuit (BAOMP) [171], Chaining Pursuit (CP) [172], Conjugate Gradient Iterative Hard Thresholding [173], Differential Orthogonal Matching Pursuit (D-OMP) [174], Fast Iterative Shrinkage Thresholding Algorithm (FISTA) [130], Forward-Backward Pursuit (FBP) [175], Fourier sampling algorithm [176], Hard Thresholding Pursuit [177], Heavy Hitters on Steroids (HHS) [178], Normalized Iterative Hard Thresholding [179], l p -Regularized Least-Squares Two Pass [180], Sequential Least Squares Matching Pursuit (SLSMP) [115], Sparse Adaptive Orthogonal Matching Pursuit (SpAdOMP) [181], Sparse Reconstruction by Separable Approximation (SpaRSA) [182], Stochastic Gradient Pursuit (SGP) [183], Stochastic Search Algorithms [184], Tree Search Matching Pursuit (TSMP) [185], and Vector Approximate Message Passing (VAMP) [186].…”

Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares

“…The main motivation for this is that underwater communications [61][62][63] and wireless channels are appropriately modelled as sparse channels consisting of only a few non-zero taps [64]. The existing approaches we evaluate for sparse channel estimation, besides IAA-APES, include the matching pursuit (MP), orthogonal matching pursuit (OMP) [65][66][67], and least squares matching pursuit (LSMP) [68] algorithms, which have been used for sparse channel estimation and equalization in many applications [69][70][71][72]. It is difficult to determine the stopping criterion when using matching pursuit algorithms, and user intervention is needed.…”

Cooperative positioning in underwater sensor networks

“…In this case, the sound waves propagating along the curved path may arrive before those in the direct path (this is referred to as the stratification effect in [11] and [12]). Hence, the direct path is not necessarily the first arrival (see, e.g., [10]- [12], [15] and the references therein). The direct path is not necessarily the strongest path either.…”